Abstract
In this manuscript, the injection of a homogeneous jet in a numerical tank is considered to revolve around discussing the limitation of the direct numerical simulation (DNS), to resolve the equations governing the problem of a jet emitted from the bottom of a numerical tank. The investigation has been made in the context of an unsteady, viscous, and incompressible fluid. The numerical resolution of the equations governing the problem is made by the compact Hermitian finite differences method (HFDM) high accuracy Oh2,h4 First, the numerical code used in this work is validated by comparing the profiles of the velocity components at the median of the lid-driven cavity with the results of the literature. Furthermore, to confirm the validity of the present numerical code, an evaluation of mesh domain sensitivity is assessed by comparing the numerical vertical velocity profiles for different steps of y-direction (flow direction) with the analytical solution. Afterward, the aim is to perform the nonlinear simulations of the Navier–Stokes equations in a large computational domain. Next, the goal is to characterize the instabilities associated with high Reynolds numbers when a jet is emitted from the bottom of the numerical tank.
Highlights
The importance of the numerical studies of the dynamics of jets for many industrial applications, has been attracting many engineers and researchers to investigate the instabilities of jet flows
The intention in this subsection is to analyze the dynamic properties of jet type flow, and to assess on the limitation of the compact Hermitian finite differences method (FDM) higher accuracy, to resolve the problem of jet with a concentration C emitted from a bottom of numerical tank, For that, the Equations (1)–(4) are resolved using the Hermitian finite differences method in a dimensionless rectangular domain sized
The fluid flow is described by the Navier–Stokes equations that are resolved by finite difference method (FDM) high accuracy
Summary
The importance of the numerical studies of the dynamics of jets for many industrial applications, has been attracting many engineers and researchers to investigate the instabilities of jet flows. The square jet flow characteristics have been investigated by Grinstein et al [16], Grinstein and DeVore [17], Quinn and Militzer [18], Sankar et al [19], Tsuchiya et al [20] and more recently by Ghasemi et al [21,22], proved that the initial vortex structures are the main difference between round and square jets It is worth pointing out the methods used to resolve equations governing jet flows. In light of the state-of-the-art above, the evolution and the distribution of the concentration of jets flows have been attracting attention in many engineering applications [25,26,27,28,29] For this reason, the objective at first and foremost is to study accurately the dynamic phenomenon of jet with a concentration C emitted from the bottom of the numerical tank.
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